Fuzzy Image Processing and Applications with MATLAB Book

Preface xi

Authors xv

1 Fuzzy Subsets and Operations 1

1.1 Introduction 1

1.2 Concept of Fuzzy Subsets and Membership Function 1

1.2.1 Membership Function 2

1.3 Linguistic Hedges 10

1.4 Operations on Fuzzy Sets 11

1.5 Fuzzy Relations 14

1.5.1 Composition of Two Fuzzy Relations 16

1.5.2 Fuzzy Binary Relation 17

1.5.3 Transitive Closure of Fuzzy Binary Relation 18

1.6 Summary 19

References 20

2 Image Processing in an Imprecise Environment 21

2.1 Introduction 21

2.2 Image as a Fuzzy Set 23

2.3 Fuzzy Image Processing 24

2.3.1 Foundations of Image Processing 24

2.3.1.1 Fuzzy Geometry 24

2.3.1.2 Measures of Fuzziness/Information 24

2.3.1.3 Rule-Based Systems 25

2.3.1.4 Fuzzy Clustering 25

2.3.1.5 Fuzzy Mathematical Morphology 25

2.3.1.6 Fuzzy Grammars 26

2.4 Some Applications of Fuzzy Set Theory in Image Processing 26

2.5 Summary 28

References 28

3 Fuzzy Similarity Measure, Measure of Fuzziness, and Entropy 31

3.1 Introduction 31

3.2 Fuzzy Similarity and Distance Measures 32

3.2.1 Examples of Fuzzy Distance Measures 33

3.2.2 Fuzzy Divergence 33

3.3 Examples of Similarity Measures 35

3.3.1 Measure Based on Tversky's Model 35

3.3.2 Similarity of Fuzzy Sets Based on Distance 37

3.4 Measures of Fuzziness 37

3.4.1 Index of Fuzziness 38

3.4.2 Index of Nonfuzziness 39

3.4.3 Yager's Measure 39

3.5 Fuzzy Entropy 40

3.5.1 Logarithmic Entropy 40

3.5.2 Shannon Fuzzy Entropy 40

3.5.3 Total Entropy 40

3.5.4 Hybrid Entropy 42

3.6 Geometry of Fuzzy Subsets 43

3.7 Summary 43

References 44

4 Fuzzy Image Preprocessing 45

4.1 Introduction 45

4.2 Contrast Enhancement 47

4.3 Fuzzy Image Contrast Enhancement47

4.3.1 Contrast Improvement Using an Intensification Operator 49

4.3.2 Contrast Improvement Using Fuzzy Histogram Hyperbolization 52

4.3.3 Contrast Enhancement Using Fuzzy IF-THEN Rules 53

4.3.4 Contrast Improvement Using a Fuzzy Expected Value 54

4.3.5 Locally Adaptive Contrast Enhancement 55

4.4 Filters 56

4.5 Fuzzy Filters 58

4.6 Summary 63

References 63

5 Thresholding Detection in Fuzzy Images 67

5.1 Introduction 67

5.2 Threshold Detection Methods 68

5.3 Types of Thresholding 69

5.3.1 Global Thresholding 69

5.3.2 Locally Adaptive Thresholding 70

5.3.3 Iterative Thresholding 71

5.3.4 Optimal Thresholding 71

5.3.5 Multispectral Thresholding 72

5.4 Thresholding Methods 72

5.5 Types of Fuzzy Methods 74

5.5.1 Gamma Membership Function 79

5.5.1.1 Fuzzy Divergence 80

5.5.1.2 Index of Fuzziness 82

5.5.1.3 Fuzzy Similarity Measure 83

5.6 Application of Thresholding 87

5.7 Summary 89

References 91

6 Fuzzy Match-Based Region Extraction 93

6.1 Match-Based Region Extraction 93

6.2 Back Projection Algorithm 95

6.2.1 Swain and Ballard's Back Projection Algorithm 95

6.2.2 Quadratic Confidence Back Projection 96

6.2.3 Local Histogramming 97

6.2.4 Binary Set Back Projection 97

6.2.5 Single Element Quadratic Back Projection 97

6.3 Fuzzy Region Extraction Methods 98

6.3.1 Fuzzy Similarity Measures 98

6.3.2 Fuzzy Measures in Region Extraction 100

6.4 Summary 107

References 107

7 Fuzzy Edge Detection 109

7.1 Introduction 109

7.2 Methods for Edge Detection 109

7.2.1 Thresholding-Based Methods 110

7.2.2 Boundary Method 111

7.2.3 Hough Transform Method 111

7.3 Fuzzy Methods 111

7.3.1 Fuzzy Sobel Edge Detector 112

7.3.2 Entropy-Based Fuzzy Edge Detection 113

7.3.3 Fuzzy Template Based Edge Detector 116

7.4 Summary 122

References 123

8 Fuzzy Content-Based Image Retrieval 125

8.1 Introduction 125

8.2 Color Spaces 126

8.3 Content-Based Color Image Retrieval 128

8.3.1 Global-Based Approach 128

8.3.2 Partition-Based Approach 129

8.3.3 Regional-Based Approach 130

8.4 Image Retrieval Model 130

8.5 Fuzzy-Based Image Retrieval Methods 131

8.5.1 Fuzzy Similarity-Based Retrieval Model 132

8.5.2 Color Histogram-Based Retrieval 134

8.5.3 Smoothed Histogram-Based Retrieval 134

8.5.4 Fuzzy Similarity/Tversky's Measure-Based Retrieval Method 136

8.5.4.1 Fuzzy Similarity Measures 137

8.6 Summary 142

References 142

9 Fuzzy Methods in Pattern Classification 145

9.1 Introduction 145

9.2 Decision Theoretic Pattern Classification Techniques 146

9.2.1 Preliminaries of Unsupervised Classification 148

9.3 Why a Fuzzy Classifier 151

9.3.1 Limitations of Statistical Classifiers 151

9.4 Fuzzy Set Theoretic Approach to Pattern Classification 152

9.5 Fuzzy Supervised Learning Algorithm 153

9.6 Fuzzy Partition 155

9.6.1 Pattern Classification Using a Fuzzy Similarity Measure 156

9.6.2 Fuzzy Similitude and Partitioning 156

9.7 Fuzzy Unsupervised Pattern Classification 161

9.8 Summary 163

References 163

10 Application of Fuzzy Set Theory in Remote Sensing 165

10.1 Introduction 165

10.2 Why Fuzzy Techniques in Remote Sensing 165

10.3 About the Remotely Sensed Data 166

10.4 Classification of Remotely Sensed Data 167

10.5 Fuzzy Sets in Remote Sensing Data Analysis 168

10.6 Background Work in Neuro Fuzzy Computing in Remote Sensing 169

10.7 Background Work on Fuzzy Sets in Remote Sensing 172

10.8 Segmentation of Remote Sensing Images 173

10.9 Fuzzy Multilayer Perceptron 175

10.9.1 Fusion of Fuzzy Logic with Neural Networks 176

10.9.2 Fuzzy MLP with Back-Propagation Learning 176

10.9.3 Fuzzy Back-Propagation Classifier Architecture 177

10.10 Fuzzy Counter-Propagation Network 178

10.11 Fuzzy CPN for Classification of Remotely Sensed Data 179

10.11.1 General Description of the Test Scenes 179

10.11.2 Experimental Results 181

10.12 Summary 182

References 183

11 MATLAB® Programs 185

11.1 Introduction 185

11.2 MATLAB Examples 187

Problems 201

Index 207